JournalsjemsVol. 22, No. 5pp. 1423–1474

On Kim-independence

  • Itay Kaplan

    The Hebrew University of Jerusalem, Israel

  • Nicholas Ramsey

    University of California at Berkeley, USA
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Abstract

We study NSOP theories. We define Kim-independence, which generalizes non-forking independence in simple theories and corresponds to non-forking at a generic scale. We show that Kim-independence satisfies a version of Kim’s lemma, local character, symmetry, and an independence theorem, and that moreover these properties individually characterize NSOP theories. We describe Kim-independence in several concrete theories and observe that it corresponds to previously studied notions of independence in Frobenius fields and vector spaces with a generic bilinear form.

Cite this article

Itay Kaplan, Nicholas Ramsey, On Kim-independence. J. Eur. Math. Soc. 22 (2020), no. 5, pp. 1423–1474

DOI 10.4171/JEMS/948